Dear Colin,
How about using the traditional distinction between elementary and non-elementary proofs of a mathematical assertion A? If by 'elementary proof of an assertion A belonging to the language of a mathematical theory T' we mean a proof of A carried out entirely within T, it seems to me that a proof of 'T |- A' is not elementary (in the above sense). At present we only have a non-elementary proof of Fermat Last Theorem.
Best wishes,
Gianluigi Oliveri
----Messaggio originale----
Da: frode.bjordal at ifikk.uio.no
Data: 3-ago-2013 12.39
A: "Foundations of Mathematics"<fom at cs.nyu.edu>
Ogg: Re: [FOM] Seeking sage advice on terminology
I now write thesis for theses of the system and theorem for results about the system.
Professor Dr. Frode Bjørdal
Universitetet i Oslo Universidade Federal do Rio Grande do Nortequicumque vult hinc potest accedere ad paginam virtualem meam
2013/8/1 Nik Weaver <nweaver at math.wustl.edu>
Colin,
I'm writing a book on forcing right now and have a similar issue.
The terminological distinction I am using is "theorem" versus
"metatheorem". Once that terminology is set up I don't find it
necessary to use different terms for proof of theorems and proofs
of metatheorems.
If saying "FLT is a theorem (of PA)" and "PA |- FLT is a metatheorem
(of your metatheory)" doesn't solve your problem, perhaps you could
use the term "metaproof" for a proof in the metatheory.
Nik
When I write about proofs of FLT I always have trouble finding a graceful
terminology to distinguish proving FLT in PA versus proving in proof theory
that PA |- FLT.
I don't mean the conceptual distinction is difficult. I mean I'd like
a cleaner terminology for it so i don't keep using "proof" to mean two
different things. Maybe the literature I have been reading does have
a solution but if so I have not absorbed it.
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